If radiation pressure is a pressure exerted upon any surface exposed to electromagnetic radiation then why do planets such as the ones in our solar system maintain consistent orbits? I'm guessing the pressure must be very slight but in the vacuum of space wouldn't even the slightest pressure effect the consistency of any planets orbit?
As Zakk's comment says, the radiation pressure is small compared to other perturbing effects. For example Earth's orbit is perturbed by the gravitational fields of the other planets (principally Jupiter) and this changes the orbit leading to the Milankovitch cycles. Compared to this type of relatively large effect radiation pressure is negligable.
There is an interesting effect of radiation pressure called the Yarkovsky effect, though this is pressure from photons radiated by the orbiting body not pressure of radiation from the Sun. This can significantly change the orbit of small bodies like asteroids and may be one of the ways bodies in the asteroid belt can move nearer the Sun and become Earth crossing. However the Yarkovsky effect is far too small to have any significant effect on bodies as large as planets.
This question is related to the stability of the solar system, which is an open question at the moment. Numerical analysis indicates that it exhibits chaotic behaviour, which means that perturbations of the orbits, such as the one you mention, should change the orbits considerably on appropriate time-scale, which is of order of 10 million years.